Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616025 | Journal of Mathematical Analysis and Applications | 2014 | 22 Pages |
Abstract
We consider higher order viscous Burgers' equations with generalized nonlinearity and study the associated initial value problems for given data in the L2L2-based Sobolev spaces. We introduce appropriate time weighted spaces to derive multilinear estimates and use them in the contraction mapping principle argument to prove local well-posedness for data with Sobolev regularity below L2L2. We also prove ill-posedness for this type of models and show that the local well-posedness results are sharp in some particular cases viz., when the orders of dissipation p , and nonlinearity k+1k+1, satisfy a relation p=2k+1p=2k+1.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xavier Carvajal, Mahendra Panthee,